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On the flexibility of group-equivariant convolutional neural networks
Roos, L. 2025. On the Flexibility of Group-Equivariant Convolutional Neural Networks. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/71005fe4-72f2-427b-a722-844be73ceb5c
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : Stellenbosch University
2025
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| _version_ | 1867613917862166528 |
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| access_status_str | Open Access |
| author | Roos, Lucas Johan |
| author2 | Kroon, R. S. |
| author_browse | Kroon, R. S. Roos, Lucas Johan |
| author_facet | Kroon, R. S. Roos, Lucas Johan |
| author_sort | Roos, Lucas Johan |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Roos, L. 2025. On the Flexibility of Group-Equivariant Convolutional Neural Networks. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/71005fe4-72f2-427b-a722-844be73ceb5c |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/132459 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:43:46.104Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/132459 On the flexibility of group-equivariant convolutional neural networks Roos, Lucas Johan Kroon, R. S. Stellenbosch University. Faculty of Science. Dept. of Computer Science. Convolutions (Mathematics) Neural networks (Computer science) Machine learning Transformations (Mathematics) UCTD Roos, L. 2025. On the Flexibility of Group-Equivariant Convolutional Neural Networks. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/71005fe4-72f2-427b-a722-844be73ceb5c Thesis (MSc)--Stellenbosch University, 2025. ENGLISH ABSTRACT: This thesis investigates the flexibility of group‐equivariant convolutional neural networks, which specialize conventional neural networks to encode equivariance to group transformations. Inspired by splines, we propose new metrics to assess the complexity of ReLU networks and use them to quantify and compare the flexibility of networks equivariant to different groups. Our analysis suggests that the current practice of comparing networks by fixing the number of trainable parameters unfairly affords models equivariant to larger groups additional expressivity. Instead, we advocate for comparisons based on a fixed computational budget—which we empirically show results in more similar levels of network flexibility. This approach allows one to better disentangle the impact of constraining networks to be equivariant from the increased expressivity they are typically granted in the literature, enabling one to obtain a more nuanced view of the impact of enforcing equivariance. Interestingly, our experiments indicate that enforcing equivariance to larger groups results in more complex fitted functions even when controlling for compute, despite reducing network expressivity. Additionally, we find that the specific choice of the group to which equivariance is enforced can significantly impact the flexibility of the resulting network, sometimes with specific, smaller groups exhibiting greater complexity than other larger ones. The experimental results supporting these conclusions also led us to prove a mathematical result stating that when networks are equivariant to different subgroups of the data symmetry group that are conjugate, they exhibit equivalent behavior. AFRIKAANSE OPSOMMING: Geen opsomming beskikbaar. Masters 2025-06-09T09:06:53Z 2025-06-09T09:06:53Z 2025-03 Thesis https://scholar.sun.ac.za/handle/10019.1/132459 en Stellenbosch University xx, 185 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Convolutions (Mathematics) Neural networks (Computer science) Machine learning Transformations (Mathematics) UCTD Roos, Lucas Johan On the flexibility of group-equivariant convolutional neural networks |
| title | On the flexibility of group-equivariant convolutional neural networks |
| title_full | On the flexibility of group-equivariant convolutional neural networks |
| title_fullStr | On the flexibility of group-equivariant convolutional neural networks |
| title_full_unstemmed | On the flexibility of group-equivariant convolutional neural networks |
| title_short | On the flexibility of group-equivariant convolutional neural networks |
| title_sort | on the flexibility of group equivariant convolutional neural networks |
| topic | Convolutions (Mathematics) Neural networks (Computer science) Machine learning Transformations (Mathematics) UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/132459 |
| work_keys_str_mv | AT rooslucasjohan ontheflexibilityofgroupequivariantconvolutionalneuralnetworks |